On the Identifiability of Steering Vectors in Large Language Models

Activation steering methods are widely used to control large language model behavior and are often interpreted as revealing meaningful internal representations. This interpretation assumes steering directions are identifiable and uniquely recoverable from input–output behavior. We prove that, under white-box single-layer access, steering vectors are fundamentally non-identifiable due to large equivalence classes of behaviorally indistinguishable interventions. Empirically, we show that orthogonal perturbations achieve 95–100% of the original steering efficacy with negligible effect sizes across multiple models and traits. We further identify structural assumptions of statistical independence, sparsity constraints, multi-environment validation and cross-layer consistency under which identifiability can be recovered. These results indicate that non-identifiable representations conflate stable signals with spurious correlations, undermining the reliability of drift monitoring in deployed systems.